I would like to find derivations of exp(-ik0r) respect to k in order to calculate exp(-ik1r) by using Taylor expansion:
exp(-ik1r) = (exp(-ik0r))(0) +(k1 -k0)(exp(-ik0r))(1)/1! + (k1 -k0)2(exp(-ik0r))(2)/2! + ...
This expansion converges when the value of r is relative low (0.3 - 1.2)...